Washington (CNN) -- Can Democrats and Republicans agree on terms to increase the amount of money the federal government is allowed to borrow, before Washington defaults on its financial obligations?

That question -- dry perhaps, but important to your bottom line -- took center stage once again Thursday as President Barack Obama met behind closed doors at the White House with Senate Republicans.

The president met Wednesday with Senate Democrats.

White House Press Secretary Jay Carney described Obama's meeting with the Republicans as a "productive" step forward in finding "common ground." Senate Minority Leader Mitch McConnell, R-Kentucky, said there had been a"candid exchange" of views.

Vice President Joe Biden, meanwhile, held his own set of deficit reduction talks with a bipartisan group of House and Senate leaders.

Treasury Secretary Tim Geithner has said the government is on track to hit its current debt ceiling of roughly $14.3 trillion by May 16, though he recently indicated in a letter to Congress he can keep the country out of default until August 2.

Analysts warn that a failure to reach an agreement in time to avoid a national default could have devastating consequences. Among other things, Americans could be faced with skyrocketing interest rates and a plummeting dollar. Translation: a higher cost of living.

Tea Party-backed GOP leaders, who have campaigned on an agenda of fiscal responsibility, are loath to agree to any increase in the debt ceiling without major spending cuts. Democrats have warned that any attempt to attach conditions to an increase in the ceiling is akin to playing a game of "chicken" with the nation's economy.

"The Democrats' solution to this crisis is simple: just raise the debt limit so we can maintain the status quo," McConnell said Thursday morning.

"The problem with that is that it isn't a solution. It's the avoidance of a solution. And that's not what the American people want. ... They want to see changes around here," he said.

McConnell later specified that any vote in favor of raising the debt ceiling should be accompanied by new cuts in discretionary spending over the next two years, followed by significant changes over the longer term to costly entitlement programs such as Medicare and Medicaid.

House Speaker John Boehner, R-Ohio, declared Monday that the overall size of any spending cuts has to exceed the magnitude of any debt ceiling increase.

The spending cuts should be in the "trillions, not just billions," Boehner said. The speaker declined to specify the period of time over which any spending cuts could be implemented -- a critical factor in any agreement.

Both Boehner and McConnell oppose tax hikes as part of any deal on the debt ceiling.

Congressional sources have told CNN they believe the Republican-controlled House could vote to increase the debt ceiling by approximately $2 trillion -- enough borrowing to get the federal government through the end of 2012.

"We need to come together ... to find this common ground that we need," Carney told reporters Thursday. There needs to be a "balanced approach" between spending cuts and tax increases in order to ensure that wealthier Americans share in any sacrifice tied to debt reduction, he said.

Both parties say they would like to avoid a repeat of the debate over the fiscal year 2011 budget, which wasn't resolved until a near-government shutdown in April. The two sides finally agreed to $38.5 billion in cuts as part of a deal to keep the government running through September 30.

Party leaders are also trying to come to grips with the budget for fiscal year 2012, which starts October 1. Any agreement on cuts tied to a debt ceiling increase will significantly impact negotiations over spending for the next year.

The current GOP proposal for fiscal year 2012, drafted by House Budget Committee Chairman Paul Ryan, R-Wisconsin, would set the federal government on a path to cut federal deficits by roughly $4.4 trillion over the next decade.

The most contentious parts of Ryan's blueprint revolve around its proposed changes to Medicare and Medicaid. Medicare, a major contributor to growing federal deficits, would be overhauled starting in 2022. The government would no longer directly pay bills for senior citizens in the program. Instead, recipients would choose a plan from a list of private providers, which the federal government would subsidize.

Medicaid, which provides health care for the disabled and the poor, would be transformed into a series of block grants to the states.

GOP leaders have denied reports that they are already backing away from their Medicare plan. Democrats, who control both the Senate and the White House, have repeatedly said the idea has no chance of being enacted.

Obama's plan, in contrast to Ryan's, aims to cut deficits by a combined $4 trillion over the next 12 years without significantly changing any of the major entitlements. Among other things, the president has also called for the creation of a "debt fail-safe" trigger that would impose automatic across-the-board spending cuts and tax changes in coming years if annual deficits are on track to exceed 2.8% of the nation's gross domestic product.

The president also wants to repeal the Bush-era tax cuts on families making more than $250,000 -- a move strongly opposed by Republicans.